Velocity-Vorticity Simulation of Unsteady 3-D Viscous Flow within a Driven Cavity

The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

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Numerical Simulation of Viscous Flow in a 3D Lid-Driven Cavity Using Lattice Boltzmann Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.444-445.395 ◽

2013 ◽

Vol 444-445 ◽

pp. 395-399

Author(s):

Di Bo Dong ◽

Sheng Jun Shi ◽

Zhen Xiu Hou ◽

Wei Shan Chen

Keyword(s):

Reynolds Number ◽

Viscous Flow ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Three Dimensional ◽

Primary Vortex ◽

Driven Cavity ◽

Single Relaxation Time ◽

Moderate Reynolds Number ◽

Boltzmann Method

A lattice Boltzmann method (LBM) with single-relaxation time and on-site boundary condition is used for the simulation of viscous flow in a three-dimensional (3D) lid-driven cavity. Firstly, this algorithm is validated by compared with the benchmark experiments for a standard cavity, and then the results of a cubic cavity with different inflow angles are presented. Steady results presented are for the inflow angle of and, and the Reynolds number is selected as 500. It is found that for viscous flow under moderate Reynolds number, there exists a primary vortex near the center and a secondly vortex at the lower right corner on each slice when, namely in a standard 3D lid-driven cavity, which cant be found when. So it can be thought that the flow pattern in a 3D lid-driven cavity depends not only on the Reynolds number but also the inflow angle.

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A numerical method for viscous flow in a driven cavity with heat and concentration sources placed on its side wall

Journal of Applied Mathematics and Computational Mechanics ◽

10.17512/jamcm.2018.3.02 ◽

2018 ◽

Vol 17 (3) ◽

pp. 17-30

Author(s):

Vusala Ambethkar ◽

Lakshmi Rani Basumatary

Keyword(s):

Viscous Flow ◽

Numerical Method ◽

Side Wall ◽

Driven Cavity

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SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization

Water ◽

10.3390/w13030245 ◽

2021 ◽

Vol 13 (3) ◽

pp. 245

Author(s):

Antonio Eirís ◽

Luis Ramírez ◽

Javier Fernández-Fidalgo ◽

Iván Couceiro ◽

Xesús Nogueira

Keyword(s):

Viscous Flow ◽

Optimal Order ◽

A Posteriori ◽

Riemann Problems ◽

Driven Cavity ◽

Flux Limiter ◽

Ideal Gases ◽

Weakly Compressible ◽

Order Variable ◽

Convective Fluxes

A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.

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Movement and deposition of fibers in an airway with steady viscous flow

International Journal of Multiphase Flow ◽

10.1016/s0301-9322(97)88125-6 ◽

1996 ◽

Vol 22 ◽

pp. 93

Author(s):

B Asgharian

Keyword(s):

Viscous Flow

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Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid

International Journal of Multiphase Flow ◽

10.1016/s0301-9322(97)88146-3 ◽

1996 ◽

Vol 22 ◽

pp. 95

Author(s):

A Mohamad

Keyword(s):

Heat Transfer ◽

Stratified Fluid ◽

Driven Cavity ◽

Flow And Heat Transfer

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Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.3.2020.26.0571 ◽

2020 ◽

Vol 14 (3) ◽

pp. 7269-7281

Author(s):

El Amin Azzouz ◽

Samir Houat

Keyword(s):

Velocity Ratio ◽

Two Dimensional ◽

Lower Side ◽

Square Cavity ◽

Driven Cavity ◽

Parallel Motion ◽

Bottom Cavity ◽

Secondary Vortices ◽

Volume Method ◽

Fluid Characteristics

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

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